Mixture

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Joy Shaha: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu May 05, 2016 4:20 am; Thanked: 3 times

by Joy Shaha » Mon Jul 11, 2016 5:53 am

Q. Four liters of milk are to be poured into a 2 liter bottle and a liter bottle .if each bottle is to be filled to the same fraction of its capacity, how many liters of milk should be poured into the 4 liter bottle ?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

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Source: Beat The GMAT — Problem Solving | Mon Jul 11, 2016 5:53 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 11, 2016 7:34 am

I believe that the problem should read as follows:

Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?

A. 2/3
B. 7/3
C. 5/2
D. 8/3
E. 3

We can PLUG IN THE ANSWERS, which represent the amount of milk that should be poured into the 4-cup bottle.

Answer choice D: 8/3
Fraction filled of the 4-cup bottle = (8/3)/4 = 2/3.
Remaining milk to be poured into the 2-cup bottle = 4 - 8/3 = 4/3.
Fraction filled of the 2-cup bottle = (4/3)/2 = 2/3.
Success!

The correct answer is D.

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Danny@GMATAcademy: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Jun 28, 2016 6:39 amFollowed by: 3 members; Thanked: 8 times; GMAT Score:780

by Danny@GMATAcademy » Mon Jul 11, 2016 7:54 am

(Number of liters in 2-liter bottle) + (Number of liters in 4-liter bottle) = 4 liters.

if x = fraction of each bottle that ends up filled, the equation above can be rewritten:

x(2) + x(4) = 4
x(2 + 4) = 4
x(6) = 4
x = 2/3

so each bottle is filled to 2/3 of its capacity.

Therefore the 4L bottle has (2/3)(4) = 8/3 Liters.

Or, conceptually:

our total capacity is 6 Liters. We put in 4 Liters altogether. So we end up filling 4/6 = 2/3 of our capacity.

Since each bottle is filled to the same fraction, each bottle will be filled to 2/3. Therefore the 4L bottle has (2/3)(4) = 8/3 Liters.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 11, 2016 8:50 am

Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?

(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

This is a clever way of telling us to take 4 cups of milk and divide it into a 1:2 ratio.
Here's why: in order to fill both bottles to the same fraction of their capacity, we need to put 2 drops of milk in the big bottle for every 1 drop of milk in the small bottle (since the big bottle has twice the capacity of the small bottle).

To divide 4 cups of milk into a 1:2 ratio, first add 1+2 to get 3.
Now take the 4 cups and divide it into 3 parts. So, we get 4/3, 4/3, 4/3
Divide the 3 parts into 1:2 = 4/3 : 4/3 + 4/3
Simplify to get: 4/3 : 8/3

So, the big bottle gets 8/3 cups = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Mon Jul 11, 2016 8:40 pm

Joy Shaha wrote:Q. Four liters of milk are to be poured into a 2 liter bottle and a 4 liter bottle .if each bottle is to be filled to the same fraction of its capacity, how many liters of milk should be poured into the 4 liter bottle ?
(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

I have taken the liberty to correct the question.
Given: 4 litres of milk and two empty bottles. One of 2 litres and another of 4 litres.

Total milk = 4 litres.
Total space = 6 litres.

Hence each bottle will be filled to 2/3rd capacity.
Quantity of milk in 4 litres bottle = 4*(2/3) = 8/3 litres

Correct option: D

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